Question 273: Ray Optics

Question

A container contains a liquid with refractive index of 1.2 up to a height of 60 cm and another liquid having refractive index 1.6 is added to height H above first liquid. If viewed from above, the apparent shift in the position of bottom of container is 40 cm . The value of H is ________ cm . (Consider liquids are immisible)

Accepted Answer

$$\begin{aligned}
& y=	ext { apparent depth of bottom } \
& \frac{y}{1}=\frac{H}{1.6}+\frac{60}{1.2} \
& 	ext { Shift }=40 \
& H+60-y=40 \
& H+60-\frac{\mathrm{H}}{1.6}-\frac{60}{1.2}=40 \
& \frac{6}{16} \mathrm{H}=30 \
& H=80 \mathrm{~cm}
\end{aligned}$$

Ray Optics

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